The transmission rate of the existing atmospheric optical communication systems can be improved using the faster-than-Nyquist transmission technology; however, atmospheric turbulence will considerably affect the system performance. Therefore, in this study, expressions are derived for obtaining the average bit error rate and average capacity of the faster-than-Nyquist atmospheric optical communication systems under a Gamma-Gamma atmospheric turbulence channel. Further, the effects of the turbulence intensity, transmission distance, and acceleration constant on the system performance are discussed. The Monte-Carlo simulation results demonstrate that the average capacity of the system can be improved using the faster-than-Nyquist transmission technology. In addition, the increasing transmission distance and decreasing acceleration constant significantly affect the bit error rate and average capacity of the system. Under the weak turbulence channel condition, the average capacity of the system using the faster-than-Nyquist transmission technology is better than 31% of the system without this technology when the acceleration constant is 0.75 and the signal-to-noise ratio is 18 dB.